<< Chapter < Page Chapter >> Page >

The error bound formula for a population mean when the population standard deviation is known is
EBM = ( z α 2 ) ( σ n ) .

The formula for sample size is n = z 2 σ 2 E B M 2 , found by solving the error bound formula for n .

In this formula, z is z α 2 , corresponding to the desired confidence level. A researcher planning a study who wants a specified confidence level and error bound can use this formula to calculate the size of the sample needed for the study.

The population standard deviation for the age of Foothill College students is 15 years. If we want to be 95% confident that the sample mean age is within two years of the true population mean age of Foothill College students, how many randomly selected Foothill College students must be surveyed?

  • From the problem, we know that σ = 15 and EBM = 2.
  • z = z 0.025 = 1.96, because the confidence level is 95%.
  • n = z 2 σ 2 E B M 2 = ( 1.96 ) 2 ( 15 ) 2 2 2 = 216.09 using the sample size equation.
  • Use n = 217: Always round the answer UP to the next higher integer to ensure that the sample size is large enough.

Therefore, 217 Foothill College students should be surveyed in order to be 95% confident that we are within two years of the true population mean age of Foothill College students.

Got questions? Get instant answers now!

Try it

The population standard deviation for the height of high school basketball players is three inches. If we want to be 95% confident that the sample mean height is within one inch of the true population mean height, how many randomly selected students must be surveyed?

35 students

Got questions? Get instant answers now!

References

“American Fact Finder.” U.S. Census Bureau. Available online at http://factfinder2.census.gov/faces/nav/jsf/pages/searchresults.xhtml?refresh=t (accessed July 2, 2013).

“Disclosure Data Catalog: Candidate Summary Report 2012.” U.S. Federal Election Commission. Available online at http://www.fec.gov/data/index.jsp (accessed July 2, 2013).

“Headcount Enrollment Trends by Student Demographics Ten-Year Fall Trends to Most Recently Completed Fall.” Foothill De Anza Community College District. Available online at http://research.fhda.edu/factbook/FH_Demo_Trends/FoothillDemographicTrends.htm (accessed September 30,2013).

Kuczmarski, Robert J., Cynthia L. Ogden, Shumei S. Guo, Laurence M. Grummer-Strawn, Katherine M. Flegal, Zuguo Mei, Rong Wei, Lester R. Curtin, Alex F. Roche, Clifford L. Johnson. “2000 CDC Growth Charts for the United States: Methods and Development.” Centers for Disease Control and Prevention. Available online at http://www.cdc.gov/growthcharts/2000growthchart-us.pdf (accessed July 2, 2013).

La, Lynn, Kent German. "Cell Phone Radiation Levels." c|net part of CBX Interactive Inc. Available online at http://reviews.cnet.com/cell-phone-radiation-levels/ (accessed July 2, 2013).

“Mean Income in the Past 12 Months (in 2011 Inflaction-Adjusted Dollars): 2011 American Community Survey 1-Year Estimates.” American Fact Finder, U.S. Census Bureau. Available online at http://factfinder2.census.gov/faces/tableservices/jsf/pages/productview.xhtml?pid=ACS_11_1YR_S1902&prodType=table (accessed July 2, 2013).

Questions & Answers

IMAGESNEWSVIDEOS A Dictionary of Computing. measures of location Quantities that represent the average or typical value of a random variable (compare measures of variation). They are either properties of a probability distribution or computed statistics of a sample. Three important measures are the mean, median, and mode.
Ahmed Reply
define the measures of location
Kaynaat Reply
IMAGESNEWSVIDEOS A Dictionary of Computing. measures of location Quantities that represent the average or typical value of a random variable (compare measures of variation). They are either properties of a probability distribution or computed statistics of a sample. Three important measures are th
Ahmed
what is confidence interval estimate and its formula in getting it
Jhezarie Reply
discuss the roles of vital and health statistic in the planning of health service of the community
BITRUS Reply
given that the probability of
BITRUS
can man city win Liverpool ?
Emmanuel Reply
There are two coins on a table. When both are flipped, one coin land on heads eith probability 0.5 while the other lands on head with probability 0.6. A coin is randomly selected from the table and flipped. (a) what is probability it lands on heads? (b) given that it lands on tail, what is the Condi
Nusrat Reply
0.5*0.5+0.5*0.6
Ravasz
what is gradient descent?
Saurav Reply
It should be a Machine learning terms。
Mok
it is a term used in linear regression
Saurav
what are the differences between standard deviation and variancs?
Enhance
what is statistics
Emmanuel Reply
statistics is the collection and interpretation of data
Enhance
the science of summarization and description of numerical facts
Enhance
Is the estimation of probability
Zaini
mr. zaini..can u tell me more clearly how to calculated pair t test
Haai
do you have MG Akarwal Statistics' book Zaini?
Enhance
Haai how r u?
Enhance
maybe .... mathematics is the science of simplification and statistics is the interpretation of such values and its implications.
Miguel
can we discuss about pair test
Haai
what is outlier?
Usama Reply
outlier is an observation point that is distant from other observations.
Gidigah
what is its effect on mode?
Usama
Outlier  have little effect on the mode of a given set of data.
Gidigah
How can you identify a possible outlier(s) in a data set.
Daniel
The best visualisation method to identify the outlier is box and wisker method or boxplot diagram. The points which are located outside the max edge of wisker(both side) are considered as outlier.
Akash
@Daniel Adunkwah - Usually you can identify an outlier visually. They lie outside the observed pattern of the other data points, thus they're called outliers.
Ron
what is completeness?
Muhammad
I am new to this. I am trying to learn.
Dom
I am also new Dom, welcome!
Nthabi
thanks
Dom
please my friend i want same general points about statistics. say same thing
alex
outliers do not have effect on mode
Meselu
also new
yousaf
I don't get the example
Hadekunle Reply
ways of collecting data at least 10 and explain
Ridwan Reply
Example of discrete variable
Bada Reply
sales made monthly.
Gbenga
I am new here, can I get someone to guide up?
alayo
dies outcome is 1, 2, 3, 4, 5, 6 nothing come outside of it. it is an example of discrete variable
jainesh
continue variable is any value value between 0 to 1 it could be 4digit values eg 0.1, 0.21, 0.13, 0.623, 0.32
jainesh
How to answer quantitative data
Alhassan Reply
hi
Kachalla
what's up here ... am new here
Kachalla
sorry question a bit unclear...do you mean how do you analyze quantitative data? If yes, it depends on the specific question(s) you set in the beginning as well as on the data you collected. So the method of data analysis will be dependent on the data collecter and questions asked.
Bheka
how to solve for degree of freedom
saliou
Quantitative data is the data in numeric form. For eg: Income of persons asked is 10,000. This data is quantitative data on the other hand data collected for either make or female is qualitative data.
Rohan
*male
Rohan
Degree of freedom is the unconditionality. For example if you have total number of observations n, and you have to calculate variance, obviously you will need mean for that. Here mean is a condition, without which you cannot calculate variance. Therefore degree of freedom for variance will be n-1.
Rohan
data that is best presented in categories like haircolor, food taste (good, bad, fair, terrible) constitutes qualitative data
Bheka
vegetation types (grasslands, forests etc) qualitative data
Bheka
I don't understand how you solved it can you teach me
Caleb Reply
solve what?
Ambo
mean
Vanarith
What is the end points of a confidence interval called?
ZIMKHITHA Reply
lower and upper endpoints
Bheka

Get the best Introductory statistics course in your pocket!





Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Introductory statistics' conversation and receive update notifications?

Ask